Answer:
A general line is written as:
y = a*x + b
where:
a is the slope
b is the y-intercept.
a) y-intercept = 2 and slope = 7.
This line is:
y = 7*x + 2
b) y-intercept = -1 and is parallel to y= 5x - 7.
Now, if two linear equations are parallel if they have the same slope and different y-intercept. Then if we want a line parallel to y= 5x - 7, this means that the slope of this line must also be equal to 5.
y = 5*x + (-1)
c) y-intercept 2 and is inclined at 45° to the x- axis.
When we have an inclination of A degrees from the x-axis, the slope of the equation is given by: a = Tan(A)
In this case, we have A = 45°
Then the slope is a = Tan(45°) = 1
Then the equation of this line is:
y = 1*x + 2
Answer:
C
Step-by-step explanation:
A function means that a graph cannot have repeating x values, so to test if something is a function we do the horizontal line test. You simply draw a vertical line and if the graph touches it twice it is not a function.
a) The point-slope form of the equation of a line through point (h, k) with slope m is
y - k = m(x - h)
In point-slope form, the equation of the line through (-3, -7) with slope -6/5 is
y + 7 = (-6/5)(x + 3)b) The graph of
y = |x|-4
represents a
translation downward 4 units of the graph of
y = |x|
It
retains the same general shape and axis of symmetry, but will have two (2) x-intercepts instead of one (1).
Answer:
(C) f’(c) = 0 and f”(c) > 0
Step-by-step explanation:
A minimum occurs where the first derivative is 0 (the tangent line is horizontal), and the second derivative is positive (concave up). The simplest example of this is a positive parabola, like y = x², which has a relative minimum at its vertex.
-40/80 = -1/2
since when you’re multiplying fraction, you multiply the top by the top number and bottom by the bottom number. So -4 • 10 is -40 and 5 • 16 is 80. -40/80, simplified is -1/2.
